If (x + 1/x)^2 = 98, compute x^2 + 1/x^2.

GATE 2014 · General Aptitude · Numerical Computation · easy

Answer: x^2 + 1/x^2 = 96

1. Expand (x + 1/x)^2: (x + 1/x)^2 = x^2 + 2 + 1/x^2. Since (x + 1/x)^2 = 98, we have x^2 + 2 + 1/x^2 = 98.
2. Solve for x^2 + 1/x^2: x^2 + 1/x^2 = 98 - 2 = 96.